Ricci-Flat Holonomy: a Classification

Details Ricci-Flat Holonomy: a Classification Ricci-Flat Holonomy: a Classification

2006-02-27

arxiv.org/abs/math/0602619v2

Mathematics

Differential Geometry

24 pages, slight corrections and presentation changes

Scientific paper

10.1016/j.geomphys.2006.12.003

The reductive holonomy algebras for a torsion-free affine connection are analysed, with the goal of establishing which ones can correspond to a Ricci-flat connection with the same properties. Various families of holonomies are eliminated through different algebraic means, and examples are constructed (in this paper and in `Projective Geometry II: Holonomy Classification', by the same author) in the remaining cases, thus solving this problem completely, for reductive holonomy.

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